arXiv subjects

Erfan Yazdandoost Hamedani

Publications and source records attributed to Erfan Yazdandoost Hamedani.

27 records · Page 2Linked to original sources

arXiv2023

A Conditional Gradient-based Method for Simple Bilevel Optimization with Convex Lower-level Problem

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem. Several iterative methods have been developed for tackling this class of problems. Alas, their convergence guarantees are either asymptotic for the upper-level objective, or the convergence rates are slow and sub-optimal. To address this issue, in this paper, we introduce a novel bilevel optimization method that locally approximates the solution set of the lower-level problem via a cutting plane, and then runs a conditional gradient update to decrease the upper-level objective. When the upper-level objective is convex, we show that our method requires ${\mathcal{O}}(\max\{1/ε_f,1/ε_g\})$ iterations to find a solution that is $ε_f$-optimal for the upper-level objective and $ε_g$-optimal for the lower-level objective. Moreover, when the upper-level objective is non-convex, our method requires ${\mathcal{O}}(\max\{1/ε_f^2,1/(ε_fε_g)\})$ iterations to find an $(ε_f,ε_g)$-optimal solution. We also prove stronger convergence guarantees under the Hölderian error bound assumption on the lower-level problem. To the best of our knowledge, our method achieves the best-known iteration complexity for the considered class of bilevel problems.

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arXiv2023

An Accelerated Asynchronous Distributed Method for Convex Constrained Optimization Problems

We consider a class of multi-agent cooperative consensus optimization problems with local nonlinear convex constraints where only those agents connected by an edge can directly communicate, hence, the optimal consensus decision lies in the intersection of these private sets. We develop an asynchronous distributed accelerated primal-dual algorithm to solve the considered problem. The proposed scheme is the first asynchronous method with an optimal convergence guarantee for this class of problems, to the best of our knowledge. In particular, we provide an optimal convergence rate of $\mathcal{O(1/K)}$ for suboptimality, infeasibility, and consensus violation.

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arXiv2022

A Decentralized Primal-dual Method for Constrained Minimization of a Strongly Convex Function

We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific convex functions over conic constraint sets defined by agent-specific nonlinear functions; hence, the optimal consensus decision should lie in the intersection of these private sets. Under the strong convexity assumption, we provide convergence rates for sub-optimality, infeasibility, and consensus violation in terms of the number of communications required; examine the effect of underlying network topology on the convergence rates.

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arXiv2021

A Stochastic Variance-reduced Accelerated Primal-dual Method for Finite-sum Saddle-point Problems

In this paper, we propose a variance-reduced primal-dual algorithm with Bregman distance for solving convex-concave saddle-point problems with finite-sum structure and nonbilinear coupling function. This type of problems typically arises in machine learning and game theory. Based on some standard assumptions, the algorithm is proved to converge with oracle complexity of $O\left(\frac{\sqrt n}ε\right)$ and $O\left(\frac{n}{\sqrt ε}+\frac{1}{ε^{1.5}}\right)$ using constant and non-constant parameters, respectively where $n$ is the number of function components. Compared with existing methods, our framework yields a significant improvement over the number of required primal-dual gradient samples to achieve $ε$-accuracy of the primal-dual gap. We tested our method for solving a distributionally robust optimization problem to show the effectiveness of the algorithm.

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arXiv2020

A Primal-Dual Algorithm with Line Search for General Convex-Concave Saddle Point Problems

In this paper, we propose a primal-dual algorithm with a novel momentum term using the partial gradients of the coupling function that can be viewed as a generalization of the method proposed by Chambolle and Pock in 2016 to solve saddle point problems defined by a convex-concave function $\mathcal L(x,y)=f(x)+Φ(x,y)-h(y)$ with a general coupling term $Φ(x,y)$ that is not assumed to be bilinear. Assuming $\nabla_xΦ(\cdot,y)$ is Lipschitz for any fixed $y$, and $\nabla_yΦ(\cdot,\cdot)$ is Lipschitz, we show that the iterate sequence converges to a saddle point; and for any $(x,y)$, we derive error bounds in terms of $\mathcal L(\bar{x}_k,y)-\mathcal L(x,\bar{y}_k)$ for the ergodic sequence $\{\bar{x}_k,\bar{y}_k\}$. In particular, we show $\mathcal O(1/k)$ rate when the problem is merely convex in $x$. Furthermore, assuming $Φ(x,\cdot)$ is linear for each fixed $x$ and $f$ is strongly convex, we obtain the ergodic convergence rate of $\mathcal O(1/k^2)$ -- we are not aware of another single-loop method in the related literature achieving the same rate when $Φ$ is not bilinear. Finally, we propose a backtracking technique which does not require the knowledge of Lipschitz constants while ensuring the same convergence results. We also consider convex optimization problems with nonlinear functional constraints and we show that using the backtracking scheme, the optimal convergence rate can be achieved even when the dual domain is unbounded. We tested our method against other state-of-the-art first-order algorithms and interior-point methods for solving quadratically constrained quadratic problems with synthetic data, the kernel matrix learning, and regression with fairness constraints arising in machine learning.

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arXiv2019

A distributed ADMM-like method for resource sharing over time-varying networks

We consider cooperative multi-agent resource sharing problems over time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific composite convex functions subject to a conic constraint that couples agents' decisions. We propose a distributed primal-dual algorithm DPDA-D to solve the saddle point formulation of the sharing problem on time-varying (un)directed communication networks; and we show that primal-dual iterate sequence converges to a point defined by a primal optimal solution and a consensual dual price for the coupling constraint. Furthermore, we provide convergence rates for suboptimality, infeasibility and consensus violation of agents' dual price assessments; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithm; and compare DPDA-D with a centralized method on the basis pursuit denoising and multi-channel power allocation problems.

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arXiv2017

Multi-agent constrained optimization of a strongly convex function over time-varying directed networks

We consider cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific possibly non-smooth composite convex functions over agent-specific private conic constraint sets; hence, the optimal consensus decision should lie in the intersection of these private sets. Assuming the sum function is strongly convex, we provide convergence rates in suboptimality, infeasibility and consensus violation; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithms.

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arXiv2016

A primal-dual method for conic constrained distributed optimization problems

We consider cooperative multi-agent consensus optimization problems over an undirected network of agents, where only those agents connected by an edge can directly communicate. The objective is to minimize the sum of agent-specific composite convex functions over agent-specific private conic constraint sets; hence, the optimal consensus decision should lie in the intersection of these private sets. We provide convergence rates both in sub-optimality, infeasibility and consensus violation; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithms; and show how to extend these methods to handle time-varying communications networks and to solve problems with resource sharing constraints.

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arXiv2014

Inverse Quadratic Transportation Problem

Many research has been conducted about quadratic programming and inverse optimization. In this paper we present the combination aspect of these subjects, applying on transportation problem. First, we obtain the inverse form of quadratic tranportation problem under $L_1$ norm by using duality as well as introducing the optimal value. Then, we do the same process for inverse quadratic transportation problem (IQTP) under $L_\infty$ norm.

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